$ x=2 a t^2 $ Differentiating both sides w.r.t. $t$, we get $ \begin{aligned} & \frac{d x}{d t}=4 a t \\ & y=a t^4 \end{aligned} $ Differentiating both sides w.r.t. t, we get $ \begin{aligned} & \frac{d y}{d t}=4 a t^3 \\ & \therefore \frac{d y}{d x}=\frac{\left(\frac{d y}{d t}\right)}{\left(\frac{d y}{d t}\right)}=\frac{4 a t^3}{4 a t}=t^2 \end{aligned} $
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